Question

求(x^2+1)/(x^4+1)的不定积分

Answer 1

积分:(x^2+1)/(x^4+1)dx

=积分:(1+1/x^2)/(x^2+1/x^2)dx(上下同时除以x^2)

=积分:d(x-1/x)/[(x-1/x)^2+(根号2)^2]

=1/根号2*arctan[(x-1/x)/根号2]+C

=1/根号2*arctan[(x^2-1)/(x根号2)]+C

(C为常数)